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Chords of migration

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Below are listed the dyadic chords of 11-limit migration temperament. Typing the chords requires consideration of the fact that migration conflates 9/8 and 10/9 and also 11/10 and 12/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 9/8 and 16/9.

Chords requiring tempering only by 81/80 are labeled didymic, by 121/120 biyatismic, by 176/175 valinorsmic, by 243/242 rastmic, and by 385/384 keenanismic. Chords which require any two of 81/80, 121/120 or 243/242 are labeled urania, and any two of 121/120, 176/175 or 385/384 zeus.

Migration has MOS of size 7, 10, 17, 24, 31, 55 and 86. Even the seven-note MOS, which is itself an essentially tempered chord, has for that reason quite a few chords, they become much more abundant with ten notes.

Triads

Number
 Chord
 Transversal
 Type
1
 0-1-2
 1-11/9-3/2
 rastmic
2
 0-1-3
 1-11/9-20/11
 biyatismic
3
 0-2-3
 1-3/2-20/11
 biyatismic
4
 0-1-4
 1-11/9-10/9
 otonal
5
 0-2-4
 1-3/2-9/8
 ambitonal
6
 0-3-4
 1-20/11-10/9
 utonal
7
 0-1-5
 1-11/9-11/8
 utonal
8
 0-2-5
 1-3/2-11/8
 otonal
9
 0-3-5
 1-20/11-11/8
 biyatismic
10
 0-4-5
 1-9/8-11/8
 otonal
11
 0-1-6
 1-11/9-5/3
 biyatismic
12
 0-2-6
 1-3/2-5/3
 otonal
13
 0-3-6
 1-20/11-5/3
 utonal
14
 0-4-6
 1-10/9-5/3
 utonal
15
 0-5-6
 1-11/8-5/3
 biyatismic
16
 0-2-8
 1-3/2-5/4
 otonal
17
 0-3-8
 1-20/11-5/4
 utonal
18
 0-4-8
 1-9/8-5/4
 otonal
19
 0-5-8
 1-11/8-5/4
 otonal
20
 0-6-8
 1-5/3-5/4
 utonal
21
 0-3-11
 1-20/11-8/7
 valinorsmic
22
 0-5-11
 1-11/8-8/7
 keenanismic
23
 0-6-11
 1-5/3-8/7
 keenanismic
24
 0-8-11
 1-5/4-8/7
 valinorsmic
25
 0-2-13
 1-3/2-12/7
 utonal
26
 0-5-13
 1-11/8-12/7
 keenanismic
27
 0-8-13
 1-5/4-12/7
 keenanismic
28
 0-11-13
 1-8/7-12/7
 otonal
29
 0-2-15
 1-3/2-9/7
 utonal
30
 0-4-15
 1-9/8-9/7
 utonal
31
 0-11-15
 1-8/7-9/7
 otonal
32
 0-13-15
 1-12/7-9/7
 otonal
33
 0-1-16
 1-11/9-11/7
 utonal
34
 0-3-16
 1-20/11-11/7
 biyatismic
35
 0-5-16
 1-11/8-11/7
 utonal
36
 0-8-16
 1-5/4-11/7
 valinorsmic
37
 0-11-16
 1-8/7-11/7
 otonal
38
 0-13-16
 1-12/7-11/7
 otonal
39
 0-15-16
 1-9/7-11/7
 otonal
40
 0-3-19
 1-20/11-10/7
 utonal
41
 0-4-19
 1-10/9-10/7
 utonal
42
 0-6-19
 1-5/3-10/7
 utonal
43
 0-8-19
 1-5/4-10/7
 utonal
44
 0-11-19
 1-8/7-10/7
 otonal
45
 0-13-19
 1-12/7-10/7
 otonal
46
 0-15-19
 1-9/7-10/7
 otonal
47
 0-16-19
 1-11/7-10/7
 otonal

Tetrads

Number
 Chord
 Transversal
 Type
1
 0-1-2-3
 1-11/9-3/2-20/11
 urania
2
 0-1-2-4
 1-11/9-3/2-9/8
 urania
3
 0-1-3-4
 1-11/9-20/11-9/8
 urania
4
 0-2-3-4
 1-3/2-20/11-9/8
 urania
5
 0-1-2-5
 1-11/9-3/2-11/8
 urania
6
 0-1-3-5
 1-11/9-20/11-11/8
 biyatismic
7
 0-2-3-5
 1-3/2-20/11-11/8
 biyatismic
8
 0-1-4-5
 1-11/9-9/8-11/8
 didymic
9
 0-2-4-5
 1-3/2-9/8-11/8
 otonal
10
 0-3-4-5
 1-20/11-9/8-11/8
 urania
11
 0-1-2-6
 1-11/9-3/2-5/3
 urania
12
 0-1-3-6
 1-11/9-20/11-5/3
 biyatismic
13
 0-2-3-6
 1-3/2-20/11-5/3
 urania
14
 0-1-4-6
 1-11/9-9/8-5/3
 urania
15
 0-2-4-6
 1-3/2-9/8-5/3
 didymic
16
 0-3-4-6
 1-20/11-10/9-5/3
 utonal
17
 0-1-5-6
 1-11/9-11/8-5/3
 biyatismic
18
 0-2-5-6
 1-3/2-11/8-5/3
 urania
19
 0-3-5-6
 1-20/11-11/8-5/3
 biyatismic
20
 0-4-5-6
 1-9/8-11/8-5/3
 urania
21
 0-2-3-8
 1-3/2-20/11-5/4
 biyatismic
22
 0-2-4-8
 1-3/2-9/8-5/4
 otonal
23
 0-3-4-8
 1-20/11-10/9-5/4
 utonal
24
 0-2-5-8
 1-3/2-11/8-5/4
 otonal
25
 0-3-5-8
 1-20/11-11/8-5/4
 biyatismic
26
 0-4-5-8
 1-9/8-11/8-5/4
 otonal
27
 0-2-6-8
 1-3/2-5/3-5/4
 ambitonal
28
 0-3-6-8
 1-20/11-5/3-5/4
 utonal
29
 0-4-6-8
 1-10/9-5/3-5/4
 utonal
30
 0-5-6-8
 1-11/8-5/3-5/4
 biyatismic
31
 0-3-5-11
 1-20/11-11/8-8/7
 zeus
32
 0-3-6-11
 1-20/11-5/3-8/7
 zeus
33
 0-5-6-11
 1-11/8-5/3-8/7
 zeus
34
 0-3-8-11
 1-20/11-5/4-8/7
 valinorsmic
35
 0-5-8-11
 1-11/8-5/4-8/7
 zeus
36
 0-6-8-11
 1-5/3-5/4-8/7
 zeus
37
 0-2-5-13
 1-3/2-11/8-12/7
 zeus
38
 0-2-8-13
 1-3/2-5/4-12/7
 keenanismic
39
 0-5-8-13
 1-11/8-5/4-12/7
 keenanismic
40
 0-5-11-13
 1-11/8-8/7-12/7
 keenanismic
41
 0-8-11-13
 1-5/4-8/7-12/7
 zeus
42
 0-2-4-15
 1-3/2-9/8-9/7
 utonal
43
 0-2-13-15
 1-3/2-12/7-9/7
 ambitonal
44
 0-11-13-15
 1-8/7-12/7-9/7
 otonal
45
 0-1-3-16
 1-11/9-20/11-11/7
 biyatismic
46
 0-1-5-16
 1-11/9-11/8-11/7
 utonal
47
 0-3-5-16
 1-20/11-11/8-11/7
 biyatismic
48
 0-3-8-16
 1-20/11-5/4-11/7
 zeus
49
 0-5-8-16
 1-11/8-5/4-11/7
 valinorsmic
50
 0-3-11-16
 1-20/11-8/7-11/7
 zeus
51
 0-5-11-16
 1-11/8-8/7-11/7
 keenanismic
52
 0-8-11-16
 1-5/4-8/7-11/7
 valinorsmic
53
 0-5-13-16
 1-11/8-12/7-11/7
 zeus
54
 0-8-13-16
 1-5/4-12/7-11/7
 zeus
55
 0-11-13-16
 1-8/7-12/7-11/7
 otonal
56
 0-11-15-16
 1-8/7-9/7-11/7
 otonal
57
 0-13-15-16
 1-12/7-9/7-11/7
 otonal
58
 0-3-4-19
 1-20/11-10/9-10/7
 utonal
59
 0-3-6-19
 1-20/11-5/3-10/7
 utonal
60
 0-4-6-19
 1-10/9-5/3-10/7
 utonal
61
 0-3-8-19
 1-20/11-5/4-10/7
 utonal
62
 0-4-8-19
 1-10/9-5/4-10/7
 utonal
63
 0-6-8-19
 1-5/3-5/4-10/7
 utonal
64
 0-3-11-19
 1-20/11-8/7-10/7
 valinorsmic
65
 0-6-11-19
 1-5/3-8/7-10/7
 keenanismic
66
 0-8-11-19
 1-5/4-8/7-10/7
 valinorsmic
67
 0-8-13-19
 1-5/4-12/7-10/7
 keenanismic
68
 0-11-13-19
 1-8/7-12/7-10/7
 otonal
69
 0-4-15-19
 1-9/8-9/7-10/7
 didymic
70
 0-11-15-19
 1-8/7-9/7-10/7
 otonal
71
 0-13-15-19
 1-12/7-9/7-10/7
 otonal
72
 0-3-16-19
 1-20/11-11/7-10/7
 biyatismic
73
 0-8-16-19
 1-5/4-11/7-10/7
 valinorsmic
74
 0-11-16-19
 1-8/7-11/7-10/7
 otonal
75
 0-13-16-19
 1-12/7-11/7-10/7
 otonal
76
 0-15-16-19
 1-9/7-11/7-10/7
 otonal

Pentads

Number
 Chord
 Transversal
 Type
1
 0-1-2-3-4
 1-11/9-3/2-20/11-9/8
 urania
2
 0-1-2-3-5
 1-11/9-3/2-20/11-11/8
 urania
3
 0-1-2-4-5
 1-11/9-3/2-9/8-11/8
 urania
4
 0-1-3-4-5
 1-11/9-20/11-9/8-11/8
 urania
5
 0-2-3-4-5
 1-3/2-20/11-9/8-11/8
 urania
6
 0-1-2-3-6
 1-11/9-3/2-20/11-5/3
 urania
7
 0-1-2-4-6
 1-11/9-3/2-9/8-5/3
 urania
8
 0-1-3-4-6
 1-11/9-20/11-9/8-5/3
 urania
9
 0-2-3-4-6
 1-3/2-20/11-9/8-5/3
 urania
10
 0-1-2-5-6
 1-11/9-3/2-11/8-5/3
 urania
11
 0-1-3-5-6
 1-11/9-20/11-11/8-5/3
 biyatismic
12
 0-2-3-5-6
 1-3/2-20/11-11/8-5/3
 urania
13
 0-1-4-5-6
 1-11/9-9/8-11/8-5/3
 urania
14
 0-2-4-5-6
 1-3/2-9/8-11/8-5/3
 urania
15
 0-3-4-5-6
 1-20/11-9/8-11/8-5/3
 urania
16
 0-2-3-4-8
 1-3/2-20/11-9/8-5/4
 urania
17
 0-2-3-5-8
 1-3/2-20/11-11/8-5/4
 biyatismic
18
 0-2-4-5-8
 1-3/2-9/8-11/8-5/4
 otonal
19
 0-3-4-5-8
 1-20/11-9/8-11/8-5/4
 urania
20
 0-2-3-6-8
 1-3/2-20/11-5/3-5/4
 urania
21
 0-2-4-6-8
 1-3/2-9/8-5/3-5/4
 didymic
22
 0-3-4-6-8
 1-20/11-10/9-5/3-5/4
 utonal
23
 0-2-5-6-8
 1-3/2-11/8-5/3-5/4
 urania
24
 0-3-5-6-8
 1-20/11-11/8-5/3-5/4
 biyatismic
25
 0-4-5-6-8
 1-9/8-11/8-5/3-5/4
 urania-
26
 0-3-5-6-11
 1-20/11-11/8-5/3-8/7
 zeus
27
 0-3-5-8-11
 1-20/11-11/8-5/4-8/7
 zeus
28
 0-3-6-8-11
 1-20/11-5/3-5/4-8/7
 zeus
29
 0-5-6-8-11
 1-11/8-5/3-5/4-8/7
 zeus
30
 0-2-5-8-13
 1-3/2-11/8-5/4-12/7
 zeus
31
 0-5-8-11-13
 1-11/8-5/4-8/7-12/7
 zeus
32
 0-1-3-5-16
 1-11/9-20/11-11/8-11/7
 biyatismic
33
 0-3-5-8-16
 1-20/11-11/8-5/4-11/7
 zeus
34
 0-3-5-11-16
 1-20/11-11/8-8/7-11/7
 zeus
35
 0-3-8-11-16
 1-20/11-5/4-8/7-11/7
 zeus
36
 0-5-8-11-16
 1-11/8-5/4-8/7-11/7
 zeus
37
 0-5-8-13-16
 1-11/8-5/4-12/7-11/7
 zeus
38
 0-5-11-13-16
 1-11/8-8/7-12/7-11/7
 zeus
39
 0-8-11-13-16
 1-5/4-8/7-12/7-11/7
 zeus
40
 0-11-13-15-16
 1-8/7-12/7-9/7-11/7
 otonal
41
 0-3-4-6-19
 1-20/11-10/9-5/3-10/7
 utonal
42
 0-3-4-8-19
 1-20/11-10/9-5/4-10/7
 utonal
43
 0-3-6-8-19
 1-20/11-5/3-5/4-10/7
 utonal
44
 0-4-6-8-19
 1-10/9-5/3-5/4-10/7
 utonal
45
 0-3-6-11-19
 1-20/11-5/3-8/7-10/7
 zeus
46
 0-3-8-11-19
 1-20/11-5/4-8/7-10/7
 valinorsmic
47
 0-6-8-11-19
 1-5/3-5/4-8/7-10/7
 zeus
48
 0-8-11-13-19
 1-5/4-8/7-12/7-10/7
 zeus
49
 0-11-13-15-19
 1-8/7-12/7-9/7-10/7
 otonal
50
 0-3-8-16-19
 1-20/11-5/4-11/7-10/7
 zeus
51
 0-3-11-16-19
 1-20/11-8/7-11/7-10/7
 zeus
52
 0-8-11-16-19
 1-5/4-8/7-11/7-10/7
 valinorsmic
53
 0-8-13-16-19
 1-5/4-12/7-11/7-10/7
 zeus
54
 0-11-13-16-19
 1-8/7-12/7-11/7-10/7
 otonal
55
 0-11-15-16-19
 1-8/7-9/7-11/7-10/7
 otonal
56
 0-13-15-16-19
 1-12/7-9/7-11/7-10/7
 otonal

Hexads

Number
 Chord
 Transversal
 Type
1
 0-1-2-3-4-5
 1-11/9-3/2-20/11-9/8-11/8
 urania
2
 0-1-2-3-4-6
 1-11/9-3/2-20/11-9/8-5/3
 urania
3
 0-1-2-3-5-6
 1-11/9-3/2-20/11-11/8-5/3
 urania
4
 0-1-2-4-5-6
 1-11/9-3/2-9/8-11/8-5/3
 urania
5
 0-1-3-4-5-6
 1-11/9-20/11-9/8-11/8-5/3
 urania
6
 0-2-3-4-5-6
 1-3/2-20/11-9/8-11/8-5/3
 urania
7
 0-2-3-4-5-8
 1-3/2-20/11-9/8-11/8-5/4
 urania
8
 0-2-3-4-6-8
 1-3/2-20/11-9/8-5/3-5/4
 urania
9
 0-2-3-5-6-8
 1-3/2-20/11-11/8-5/3-5/4
 urania
10
 0-2-4-5-6-8
 1-3/2-9/8-11/8-5/3-5/4
 urania
11
 0-3-4-5-6-8
 1-20/11-9/8-11/8-5/3-5/4
 urania
12
 0-3-5-6-8-11
 1-20/11-11/8-5/3-5/4-8/7
 zeus
13
 0-3-5-8-11-16
 1-20/11-11/8-5/4-8/7-11/7
 zeus
14
 0-5-8-11-13-16
 1-11/8-5/4-8/7-12/7-11/7
 zeus
15
 0-3-4-6-8-19
 1-20/11-10/9-5/3-5/4-10/7
 utonal
16
 0-3-6-8-11-19
 1-20/11-5/3-5/4-8/7-10/7
 zeus
17
 0-3-8-11-16-19
 1-20/11-5/4-8/7-11/7-10/7
 zeus
18
 0-8-11-13-16-19
 1-5/4-8/7-12/7-11/7-10/7
 zeus
19
 0-11-13-15-16-19
 1-8/7-12/7-9/7-11/7-10/7
 otonal

Septads

Number
 Chord
 Transversal
 Type
1
 0-1-2-3-4-5-6
 1-11/9-3/2-20/11-9/8-11/8-5/3
 urania
2
 0-2-3-4-5-6-8
 1-3/2-20/11-9/8-11/8-5/3-5/4
 urania